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On the Number of Cusps of Stable Perturbations of a Plane-to-Plane Singularity
Let $f:(R^{2}, O)\rightarrow(R^{2},0)$ be a smooth map germ. By the theorem of Whitney [Wh], $f$ can be approximated (in the semi-local sense) by a $C^{\infty}$ stable mapping. In other words, $f$ isExpand
Singularities of Frontals
In this survey article we introduce the notion of frontals, which provides a class of generalised submanifolds with singularities but with well-defined tangent spaces. We present a review of basicExpand
Generic singularities of implicit systems of first order differential equations on the plane
For the implicit systems of first order ordinary differential equations on the plane there is presented the complete local classification of generic singularities of family of its phase curves up toExpand
Symplectic Bifurcations of Plane Curves and Isotropic Liftings
We study the classification of varieties in the Marsden–Weinstein reduction and their liftability. In particular the complete symplectic classification of the Bruce–Gaffney plane curve singularitesExpand
Classification of generic integral diagrams and first order ordinary differential equations
An adhesive composition for plastic-metal foil composite packaging materials which comprises (A) a polyester glycol having a molecular weight of 3,000 to 100,000, a polyester-polyurethane polyolExpand
Symplectic and Lagrange stabilities of open Whitney umbrellas
In this paper we formulate and prove the criteria for the Lagrange stability of isotropic map-germs of corank at most one. They include an analogue of Mather’s characterisation of the stability ofExpand
Singularities of tangent surfaces in Cartan's split G2-geometry
In the split G2-geometry, we study the correspondence found by E. Cartan between the Cartan distribution and the contact distribution with Monge structure on spaces of five variables. Then theExpand
Openings of differentiable map-germs and unfoldings
The algebraic notion of openings of a map-germ is introduced in this paper. An opening separates the self-intersections of the original mapgerm, preserving its singularities. The notion of openingsExpand